Windows 7: Sony Vaio BSOD Screens and query on checking external drives

Sorry KoolKat, I wanted to check the drives first before doing that. I will do it now.
I have attached another diskmgmt.msc screen shot showing the 'e' drive which says it's healthy.
I just disconnected the usb to my printer and got the same BSOD as I loaded earlier.

Will do it now and report back

Try running the CHKDSK on the e: drive now, with it plugged in (how did you think it might be able to check it without being plugged in?)

I checked the 'e' drive with the usb stick attached and have posted the results below. I don't know much about computers - I didn't realise you had to have a storage device attached to the drive in order to check it. I have posted the screen shot below.
I dis-enabled driver verifier and when I was shutting down the computer having done so, windows updates were being installed and I got the same BSOD screen as was in the bugcheck earlier. I rebooted and haven't had one since. Is it safe for the computer to leave the driver verifier dis-enabled?

Microsoft Windows [Version 6.1.7601]
Copyright (c) 2009 Microsoft Corporation. All rights reserved.
C:\Windows\system32>chkdsk e:
The type of the file system is FAT32.
Volume Serial Number is 6810-485C
Windows is verifying files and folders...
File and folder verification is complete.
Windows has checked the file system and found no problems.

4,012,900,352 bytes total disk space.
323,747,840 bytes in 26 files.
3,689,119,744 bytes available on disk.

32,768 bytes in each allocation unit.
122,464 total allocation units on disk.
112,583 allocation units available on disk.

It has been one week since this post and I have not had another BSOD after dis-enabling driver verifier. I am wondering if it is safe to leave it dis-enabled? Thank you for your help and advise to date.

Like I said verifier can cause false BSOD so you're better with it disabled.